“Dynamics-aware numerical coarsening for fabrication design”

  • ©Desai Chen, David Levitt, Wojciech Matusik, and Danny M. Kaufman




    Dynamics-aware numerical coarsening for fabrication design

Session/Category Title: Dynamic Fabrication




    The realistic simulation of highly-dynamic elastic objects is important for a broad range of applications in computer graphics, engineering and computational fabrication. However, whether simulating flipping toys, jumping robots, prosthetics or quickly moving creatures, performing such simulations in the presence of contact, impact and friction is both time consuming and inaccurate. In this paper we present Dynamics-Aware Coarsening (DAC) and the Boundary Balanced Impact (BBI) model which allow for the accurate simulation of dynamic, elastic objects undergoing both large scale deformation and frictional contact, at rates up to 79 times faster than state-of-the-art methods. DAC and BBI produce simulations that are accurate and fast enough to be used (for the first time) for the computational design of 3D-printable compliant dynamic mechanisms. Thus we demonstrate the efficacy of DAC and BBI by designing and fabricating mechanisms which flip, throw and jump over and onto obstacles as requested.


    1. Steven S. An, Theodore Kim, and Doug L. James. 2008. Optimizing Cubature for Efficient Integration of Subspace Deformations. ACM Trans. Graph. 27, 5, Article 165 (Dec. 2008), 10 pages. Google ScholarDigital Library
    2. Moritz Bächer, Emily Whiting, Bernd Bickel, and Olga Sorkine-Hornung. 2014. Spin-it: Optimizing Moment of Inertia for Spinnable Objects. ACM Trans. Graph. 33, 4, Article 96 (July 2014), 10 pages.Google ScholarDigital Library
    3. Jernej Barbič and Doug L. James. 2005. Real-Time Subspace Integration for St. Venant-Kirchhoff Deformable Models. ACM Trans. Graph. 24, 3 (July 2005), 982–990. Google ScholarDigital Library
    4. Nicholas W Bartlett, Michael T Tolley, Johannes T B Overvelde, James C Weaver, Bobak Mosadegh, Katia Bertoldi, George M Whitesides, and Robert J Wood. 2015. SOFT ROBOTICS. A 3D-printed, functionally graded soft robot powered by combustion. Science 349, 6244 (July 2015), 161–165.Google ScholarCross Ref
    5. Ted Belytschko, Wing Kam Liu, Brian Moran, and Khalil Elkhodary. 2013. Nonlinear Finite Elements for Continua and Structures. John Wiley & Sons.Google Scholar
    6. Sarah Bergbreiter. 2008. Effective and efficient locomotion for millimeter-sized micro-robots. In 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems. IEEE, 4030–4035. Google ScholarCross Ref
    7. Sarah Bergbreiter and Kristofer SJ Pister. 2007. Design of an autonomous jumping micro-robot. In Proceedings 2007 IEEE International Conference on Robotics and Automation. IEEE, 447–453. Google ScholarCross Ref
    8. Miklós Bergou, Saurabh Mathur, Max Wardetzky, and Eitan Grinspun. 2007. TRACKS: Toward Directable Thin Shells. ACM Trans. Graph. 26, 3, Article 50 (July 2007), 10 pages.Google ScholarDigital Library
    9. Bernd Bickel, Peter Kaufmann, Mélina Skouras, Bernhard Thomaszewski, DerekBradley, Thabo Beeler, Phil Jackson, Steve Marschner, Wojciech Matusik, and Markus Gross. 2012. Physical face cloning. ACM Trans. Graph. 31, 4, Article 118 (July 2012), 10 pages.Google ScholarDigital Library
    10. Jeffrey T Bingham, Jeongseok Lee, Ravi N Haksar, Jun Ueda, and C Karen Liu. 2014. Orienting in mid-air through configuration changes to achieve a rolling landing for reducing impact after a fall. In 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems. IEEE, 3610–3617.Google ScholarCross Ref
    11. Desai Chen, David Levin, Wojciech Matusik, and Danny M. Kaufman. 2017. Uncut user study videos. https://www.dropbox.com/sh/5quhghwg6vjjjuz/AAAuBS8ilZ2Tisv52C_YQYrma.Google Scholar
    12. Desai Chen, David I. W. Levin, Shinjiro Sueda, and Wojciech Matusik. 2015. Data-driven Finite Elements for Geometry and Material Design. ACM Trans. Graph. 34, 4, Article 74 (July 2015), 10 pages.Google ScholarDigital Library
    13. Francisco Chinesta, Adrien Leygue, Felipe Bordeu, Jose Vicente Aguado, Elías Cueto, David González, Iciar Alfaro, Amine Ammar, and Antonio Huerta. 2013. PGD-based computational vademecum for efficient design, optimization and control. Archives of Computational Methods in Engineering 20, 1 (2013), 31–59. Google ScholarCross Ref
    14. Kyu-Jin Cho, Je-Sung Koh, Sangwoo Kim, Won-Shik Chu, Yongtaek Hong, and Sung-Hoon Ahn. 2009. Review of manufacturing processes for soft biomimetic robots. International Journal of Precision Engineering and Manufacturing 10, 3 (2009), 171–181. Google ScholarCross Ref
    15. Wayne A Churaman, Aaron P Gerratt, and Sarah Bergbreiter. 2011. First leaps toward jumping microrobots. 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2011) (2011), 1680–1686.Google ScholarCross Ref
    16. Stelian Coros, Bernhard Thomaszewski, Gioacchino Noris, Shinjiro Sueda, Moira Forberg, Robert W. Sumner, Wojciech Matusik, and Bernd Bickel. 2013. Computational Design of Mechanical Characters. ACM Trans. Graph. 32, 4, Article 83 (July 2013), 12 pages.Google ScholarDigital Library
    17. Peter Deuflhard, Rolf Krause, and Susanne Ertel. 2008. A contact-stabilized Newmark method for dynamical contact problems. Internat. J. Numer. Methods Engrg. 73, 9 (2008), 1274–1290. Google ScholarCross Ref
    18. David Doyen, Alexandre Ern, and Serge Piperno. 2011. Time-Integration Schemes for the Finite Element Dynamic Signorini Problem. SIAM Journal on Scientific Computing 33, 1 (Jan. 2011), 223–249. Google ScholarDigital Library
    19. Kris K. Hauser, Chen Shen, and James F O’Brien. 2003. Interactive Deformation Using Modal Analysis with Constraints. In Graphics Interface. CIPS, Canadian Human-Computer Commnication Society, 247–256.Google Scholar
    20. Doug L. James and Dinesh K. Pai. 2002. DyRT: Dynamic Response Textures for Real Time Deformation Simulation with Graphics Hardware. In Proceedings of the 29th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH ’02). ACM, New York, NY, USA, 582–585. Google ScholarDigital Library
    21. Gwang-Pil Jung, Ji-Suk Kim, Je-Sung Koh, Sun-pil Jung, and Kyu-Jin Cho. 2014. Role of compliant leg in the flea-inspired jumping mechanism. In 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2014). IEEE, 315–320. Google ScholarCross Ref
    22. Sun-Pill Jung, Gwang-Pil Jung, Je-Sung Koh, Dae-Young Lee, and Kyu-Jin Cho. 2015. Fabrication of Composite and Sheet Metal Laminated Bistable Jumping Mechanism. Journal of Mechanisms and Robotics 7, 2 (Feb. 2015), 021010.Google ScholarCross Ref
    23. Couro Kane, Jerrold E. Marsden, Michael Ortiz, and Matthew West. 2000. Variational integrators and the Newmark algorithm for conservative and dissipative mechanical systems. Internat. J. Numer. Methods Engrg. 49, 10 (2000), 1295–1325. Google ScholarCross Ref
    24. Couro Kane, Eduardo A. Repetto, Michael Ortiz, and Jerrold E. Marsden. 1999. Finite element analysis of nonsmooth contact. Computer Methods in Applied Mechanics and Engineering 180, 1–2 (1999), 1–26.Google ScholarCross Ref
    25. Lily Kharevych, Patrick Mullen, Houman Owhadi, and Mathieu Desbrun. 2009. Numerical Coarsening of Inhomogeneous Elastic Materials. ACM Trans. Graph. 28, 3, Article 51 (July 2009), 8 pages. Google ScholarDigital Library
    26. Je-Sung Koh, Sun pil Jung, Robert J Wood, and Kyu-Jin Cho. 2013. A jumping robotic insect based on a torque reversal catapult mechanism. In 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2013). IEEE, 3796–3801.Google Scholar
    27. Je-Sung Koh, Eunjin Yang, Gwang-Pil Jung, Sun-Pill Jung, Jae Hak Son, Sang-Im Lee, Piotr G Jablonski, Robert J Wood, Ho-Young Kim, and Kyu-Jin Cho. 2015. BIOMECHANICS. Jumping on water: Surface tension-dominated jumping of water striders and robotic insects. Science 349, 6247 (July 2015), 517–521. Google ScholarCross Ref
    28. Rolf Krause and Mirjam Walloth. 2012. Presentation and comparison of selected algorithms for dynamic contact based on the Newmark scheme. Applied Numerical Mathematics 62, 10 (Oct. 2012), 1393–1410. Google ScholarDigital Library
    29. Siwang Li, Jin Huang, Fernando de Goes, Xiaogang Jin, Hujun Bao, and Mathieu Desbrun. 2014. Space-time Editing of Elastic Motion Through Material Optimization and Reduction. ACM Trans. Graph. 33, 4, Article 108 (July 2014), 10 pages.Google ScholarDigital Library
    30. Shuguang Li, Robert Katzschmann, and Daniela Rus. 2015. A soft cube capable of controllable continuous jumping. In 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 1712–1717.Google Scholar
    31. Hod Lipson. 2014. Challenges and Opportunities for Design, Simulation, and Fabrication of Soft Robots. Soft Robotics 1, 1 (March 2014), 21–27. Google ScholarCross Ref
    32. Michael Loepfe, Christoph M Schumacher, Urs B Lustenberger, and Wendelin J Stark. 2015. An untethered, jumping roly-poly soft robot driven by combustion. Soft Robotics 2, 1 (2015), 33–41. Google ScholarCross Ref
    33. Zoltan Major, Martin Reiter, Elena Hemmeter, and Franz Hiptmair. 2011. Combination of Novel Virtual and Real Prototyping Methods in a Rapid Product Development Methodology. Polimeri 32 (2011).Google Scholar
    34. Vladimir A Mandelshtam and Howard S Taylor. 1997. Harmonic inversion of time signals and its applications. The Journal of Chemical Physics 107, 17 (Nov. 1997), 6756–6769. Google ScholarCross Ref
    35. Jerrold E. Marsden and Matthew West. 2001. Discrete mechanics and variational integrators. Acta Numerica 2001 10 (May 2001), 357–514. Google ScholarCross Ref
    36. Sebastian Martin, Peter Kaufmann, Mario Botsch, Eitan Grinspun, and Markus Gross. 2010. Unified Simulation of Elastic Rods, Shells, and Solids. ACM Trans. Graph. 29, 4, Article 39 (July 2010), 10 pages.Google ScholarDigital Library
    37. Jürgen Moser and Alexander P Veselov. 1991. Discrete versions of some classical integrable systems and factorization of matrix polynomials. Communications in Mathematical Physics 139, 2 (1991), 217–243. Google ScholarCross Ref
    38. Matthieu Nesme, Paul G. Kry, Lenka Jeřábková, and François Faure. 2009. Preserving Topology and Elasticity for Embedded Deformable Models. ACM Trans. Graph. 28, 3, Article 52 (July 2009), 9 pages. Google ScholarDigital Library
    39. Minkyun Noh, Seung-Won Kim, Sungmin An, Je-Sung Koh, and Kyu-Jin Cho. 2012. Flea-Inspired Catapult Mechanism for Miniature Jumping Robots. IEEE Transactions on Robotics 28, 5 (2012), 1007–1018. Google ScholarDigital Library
    40. Anna Pandolfi, Couro Kane, Jerrold E. Marsden, and Michael Ortiz. 2002. Time-discretized variational formulation of non-smooth frictional contact. Internat. J. Numer. Methods Engrg. 53, 8 (March 2002), 1801–1829. Google ScholarCross Ref
    41. Romain Prévost, Emily Whiting, Sylvain Lefebvre, and Olga Sorkine-Hornung. 2013. Make It Stand: Balancing Shapes for 3D Fabrication. ACM Trans. Graph. 32, 4, Article 81 (July 2013), 10 pages.Google ScholarDigital Library
    42. Pedro M. Reis. 2015. A Perspective on the Revival of Structural (In) Stability With Novel Opportunities for Function: From Buckliphobia to Buckliphilia. Journal of Applied Mechanics 82, 11 (2015), 111001.Google ScholarCross Ref
    43. Pedro M. Reis, Heinrich M. Jaeger, and Martin van Hecke. 2015. Designer Matter: A perspective. Extreme Mechanics Letters 5 (Dec. 2015), 25–29. Google ScholarCross Ref
    44. Daniela Rus and Michael T. Tolley. 2015. Design, fabrication and control of soft robots. Nature 521, 7553 (May 2015), 467–475. Google ScholarCross Ref
    45. Ahmed A Shabana. 2012. Theory of Vibration. Springer Science & Business Media, New York, NY.Google Scholar
    46. Mélina Skouras, Bernhard Thomaszewski, Stelian Coros, Bernd Bickel, and Markus Gross. 2013. Computational Design of Actuated Deformable Characters. ACM Trans. Graph. 32, 4, Article 82 (July 2013), 10 pages.Google ScholarDigital Library
    47. Bernhard Thomaszewski, Stelian Coros, Damien Gauge, Vittorio Megaro, Eitan Grinspun, and Markus Gross. 2014. Computational design of linkage-based characters. ACM Transactions on Graphics 33, 4, Article 64 (July 2014), 9 pages.Google ScholarDigital Library
    48. Rosell Torres, Alejandro Rodríguez, José M. Espadero, and Miguel A. Otaduy. 2016. High-resolution Interaction with Corotational Coarsening Models. ACM Trans. Graph. 35, 6, Article 211 (Nov. 2016), 11 pages.Google ScholarDigital Library
    49. Dominic Vella. 2015. ROBOTICS. Two leaps forward for robot locomotion. Science 349, 6247 (July 2015), 472–473. Google ScholarCross Ref
    50. Bin Wang, Longhua Wu, KangKang Yin, Uri Ascher, Libin Liu, and Hui Huang. 2015. Deformation Capture and Modeling of Soft Objects. ACM Trans. Graph. 34, 4, Article 94 (July 2015), 12 pages.Google ScholarDigital Library

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